Integers simply!

Find all the integers \(x,y,z\) satisfying

\(\large x^2 + y^2 + z^2 = 2xyz\).

Evaluate the \(\textbf{sum}\) of all integers of each pair.

\(\textbf{Details}\)

For e.g. If you get your integers solution as

\((1,2,3)\) and \((2,-1,5)\)

Then enter your answer as \(1+2+3+2-1+5=\boxed{12}\)

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